How do I add texture to new faces on an already-textured mesh?
Like someonewithpc said, you can simply create the new geometry for the fringe and add it to the existing UV map:


Create the new geometry
In Edit mode, deselect everything then select only the new geometry
With your cursor in the 3D view, type 'U' and select your preferred method of UV unrwapping
In the UV/Image Editor, select the new geometry and place it in an unused portion of the texture. (Hopefully you have some blank spots in the image. If not, you're out of luck)


The new geometry should be part of the UV map, and the existing UV map will remain unchanged.